In the conventional grating element technology, beam splitting is performed for one wavelength of a semiconductor laser by polarizing control. For example, Japanese Patent Application Laid-Open (JP-A) No. 2002-90534 (paragraph No. 17, FIG. 1, and the like) can be referred to. That is, in two modes of TE polarization and TM polarization, light is reflected in TE polarization and the light is transmitted in TM polarization. However, the conventional grating element cannot be used in two different wavelengths of semiconductor lasers.
There has also been proposed an apparatus in which Si and SiO2 are alternately laminated on a SiO2 substrate to form rectangular projections having a total of five layers and polarizing control is performed for an arbitrary angle of incidence and operation wavelength. For example, Tyan et al., “Design, fabrication, and characterization of form-birefringent multilayer polarizing beam splitter”, Vol. 14, No. 7, July J. Opt. Soc. Am. A (1997) can be referred to. JP-A No. 2001-51122 discloses a polarization beam splitter in which a phase is imparted to incident light to separate polarized electromagnetic radiations by a structure in which layers are laminated repeatedly with a period shorter than first Bragg condition. However, it is difficult to actually produce the apparatus disclosed in JP-A No. 2001-51122. Further, even if the apparatus is produced, a process is complicated and production cost is expensive.
A principle of polarization splitting by a diffraction grating will be described below. As shown in FIG. 1, the light progresses from a medium having a refractive index n1 to a medium having a refractive index n2. A grating having a period Λ is formed in a boundary.
In the light, there are two kinds of polarization which are called TE polarization (s polarization) and TM polarization (p polarization). When the light is incident to the diffraction grating, polarization in the direction in which the electric field is vibrated in parallel with a groove of the grating is called TE polarization, and the polarization in the direction in which the electric field is vibrated perpendicular to the groove (in which the magnetic field is vibrated in parallel with the groove) of the grating is called TM polarization.
When the diffraction grating satisfies the following condition of formula (1) for a wavelength λ, the light is observed in the diffraction grating structure, as if the light were traveling in a thin-film structure expressed by an effective refractive index neff:Λ cos θ0<λ  (1)where θ0 is an angle of incidence and Λ is a period. In this case, the effective refractive index neff varies depending on a polarization direction of the incident light, and the effective refractive index neff is expressed by the following formulas in first approximation.TE polarization: nTE=√{square root over ((1−f)n12+fn22)}  (2)
                              n          TM                =                                            n              1                        ⁢                          n              2                                                                          fn                1                2                            +                                                (                                      1                    -                    f                                    )                                ⁢                                  n                  2                  2                                                                                        (        3        )            where f is a ratio of a projection side part to the period Λ in FIG. 1. As can be seen from the above formulas, other than f of 0 and 1, the effective refractive index has different values for each of the polarization.
In a physical meaning of a difference in effective refractive index based on a state of polarization, when the light passes through a structure extremely smaller than the wavelength of the light, the structure is perceived as a shielding substance which generates scattering and the like. As a result, it can be thought that energy loss is generated when the light passes through the shielding substance, and an influence of the energy loss emerges in the form of the effective refractive index.
When any one of effective refractive indexes neff=nTE and neff=nTM (however, nTE≠nTM) for polarization components satisfies the following formula (4) under this condition, the incident light having the polarization direction cannot pass through the thin-film layer having the effective refractive index neff:n1 sin θ0≧neff  (4)wherein the formula (4) is deformed from a relational formula (Snell's formula) of refraction of light which progresses in different mediums. In this state, an angle of refraction θ1 substantially reaches 90° in the thin-film layer having the effective refractive index neff in FIG. 1, and the light cannot move to the layer having the refractive index n2. As a result, reflected light is generated as divergence of the incident energy.
Thus, when the formula (4) holds by the effect of the effective refractive index neff which is observed for the light having any one of the polarization directions in the grating structure, a polarizing element having the fine period is realized.
As described above, when the period is set to the wavelength or less in the grating portion, diffracted waves are not generated in the progress of the light expressed as an electromagnetic wave. Accordingly, diffraction effect expressed by superposition of waves is not observed. The grating portion is regarded as an object in which a refractive index varies for the progress of the wave, and the grating portion imparts such an effect to the electromagnetic wave as if it were traveling in a material having a virtual refractive index. As a result, the same effect as the thin-film layer is brought in a particular wavelength range. A technique of assuming that the grating portion is a material having a virtual refractive index is called effective refractive index method. For example, a formula for determining an effective refractive index from a grating shape is described in Journal of Optical Society of America A Vol. 13, No. 5, p 1013. In the layer with an effective refractive index, a value of the effective refractive index is determined by a ratio of the projection part to the period of the grating portion. The grating portion having rectangular pits and projections also depends on a particular wavelength band, and design of the gratin portion is determined by the ratio and a height of the rectangular pits and projections. For example, as disclosed in Journal of Optical Society of America A Vol. 13, No. 5, p 988, or Applied Optics Vol. 36, No. 34, p 8935, in order to widen a wavelength band, an effective refractive index can continuously be changed by forming the grating portion in triangular shape with respect to a height direction. The same performance as the effect of laminating many thin-film layers by which the change is continuously imparted, can be obtained by the operation.
However, the polarizing element having a simple structure which can be used for two wavelengths in a predetermined wavelength range has not been developed yet.